City-States keep asking me to connect to them, but I'm not sure if the life-long upkeep is worth the one-time influence gain. If, on the other hand, I get influence and an income boost, I'm gonna have to buy my workers an extra set of shovels and connect to city-states like mad.

I could, of course, just erase the roads after I make them, but that seems like a step away from the narrative of the game and the reason behind making the road in the first place.

Good question, I was wondering the same thing. To me it seems a road to a city state is only good for a one time influence boost and nothing else. I don't have any empirical evidence for this though and haven't tried removing such a road yet to see what happens.
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decezeOct 28 '10 at 3:09

Is it necessary to build a road or will any trade network connection (harbour) suffice?
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AkuseteOct 28 '10 at 4:22

2

@Akusete, given you do not get trade income, the only reasons to connect a city-state are to appease them if they ask for "a road to your capital" (which works just using a harbour, assuming the city state has one as well) or if they are an Ally you can apparently use their harbour to extend your trade network overseas (which only makes sense if you don't have a local harbour, do have a harbour on the other side of some water, and requires a road link). Or, maybe if you need to provide faster travel to/from the CS, if the CS is giving you units or you need to defend them maybe...
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DMA57361Oct 28 '10 at 9:50

How come I get notifications telling me "Citizens of [City-State] believe that we can mutually prosper from a trade route"? What is this talking about?
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JakobudJan 12 at 1:23

Now I've logged a couple hundred hours including the latest patch (which change a lot) and IMO:

The costs of maintaining a road to your loving city-state far outweighs the benefit in the long run.

I have removed roads as suggested earlier. Meh.

I had a match where it was going to take 5 tiles to connect to a city state onto the direct road, but only two from the city on the other side.. it was connected solely by a harbor for its trade route. The road I built, and Helsinki built their end of it.. did NOT trigger the expected bonus,